Although there are anticipations of the notion of the analytic in Locke and Hume in their talk of “relations of ideas,” the specific terms “analytic” and “synthetic” themselves were introduced by Kant (1781/1998) at the beginning of his Critique of Pure Reason, where he wrote:
——-ΚΑΝΤ: ΟΡΙΣΜΟΣ ΑΝΑΛΥΤΙΚΩΝ/ΣΥΝΘΕΤΙΚΩΝ ΚΡΙΣΕΩΝ———-
::: In all judgments in which the relation of a subject to the predicate is thought
(if I only consider affirmative judgments, since the application to negative ones is easy)
this relation is possible in two different ways.
Either the predicate B belongs to the subject A as something that is (covertly) contained in this concept A; or B lies entirely outside the concept A, though to be sure it stands in connection with it.
In the first case, I call the judgment analytic, in the second synthetic. (A:6-7)
——KANT: ΠΑΡΑΔΕΙΓΜΑΤΑ ΑΝΑΛΥΤΙΚΟ/ΣΥΝΘΕΤΙΚΟ—————
He provided as an example of an analytic judgment, “All bodies are extended”: in thinking of a body [[[we can’t help]]] but also think of something extended in space; that would seem to be just part of what is meant by “body.”
He contrasted this with “All bodies are heavy,” where the predicate (“is heavy”) “is something entirely different from that which I think in the mere concept of body in general” (A7), and we must put together, or “synthesize,” the different concepts, body and heavy (sometimes such concepts are called “ampliative,” “amplifying” a concept beyond what is “contained” in it).
Kant tried to spell out his “containment” metaphor for the analytic in two ways.
To see that any of set II is true, he wrote, “I need only to analyze the concept, i.e., become conscious of the manifold that I always think in it, in order to encounter this predicate therein” (A7).
But then, picking up a suggestion of Leibniz , he went on to claim:
——————ΑΝΑΛΥΤΙΚΟ/ΣΥΝΘΕΤΙΚΟ ΚΑΙ ΑΝΤΙΦΑΣΗ———-
I merely draw out the predicate in accordance with the principle of contradiction, and can thereby at the same time become conscious of the necessity of the judgment. (A7)
As Katz (1988) recently emphasized, this second definition is significantly different from the “containment” idea, since now, in its appeal to the powerful method of proof by contradiction, the analytic would include all of the (potentially infinite) deductive consequences of a particular claim, most of which could not be plausibly regarded as “contained” in the concept expressed in the claim. For starters, “Bachelors are unmarried or the moon is blue” is a logical consequence of “Bachelors are unmarried”—its denial contradicts the latter (a denial of a disjunction is a denial of each disjunct)—but clearly nothing about the color of the moon is remotely “contained in” the concept bachelor. To avoid such consequences, Katz (e.g., 1972, 1988) goes on to try to develop a serious theory based upon only the initial containment idea, as, along different lines, does Pietroski (2005).
One reason Kant may not have noticed the differences between his different characterizations of the analytic was that his conception of “logic” seems to have been confined to Aristotelian syllogistic, and so didn’t include the full resources of modern logic, where the differences between the two characterizations become more glaring (see MacFarlane 2002).
Indeed, he demarcates the category of the analytic chiefly in order to contrast it with what he regards as the more important category of the synthetic, which he famously thinks is not confined, as one might initially suppose, merely to the empirical.
While some trivial a priori claims might be analytic, for Kant the seriously interesting ones were synthetic. He argues that even so elementary an example in arithmetic as “7+5=12,” is synthetic, since the concept of “12” is not contained in the concepts of “7,” “5,” or “+,”: appreciating the truth of the proposition would seem to require some kind of active synthesis of the mind uniting the different constituent thoughts.
And so we arrive at the category of the “synthetic a priori,” whose very possibility became a major concern of his work. He tries to show that the activity of “synthesis” was the source of the important cases of a priori knowledge, not only in arithmetic, but also in geometry, the foundations of physics, ethics, and philosophy generally, a view that set the stage for much of the philosophical discussions of the subsequent century (see Coffa 1991:pt I).
Apart from geometry, Kant, himself, didn’t focus much on the case of mathematics. But, as mathematics in the 19th C. began reaching new heights of sophistication, worries were increasingly raised about its foundations as well. It was specifically in response to this latter problem that Gottlob Frege (1884/1980) tried to improve upon Kant’s formulations of the analytic, and presented what is widely regarded as the next significant discussion of the topic.